The midfielder was injured during England's 5-0 win over the Czech Republic and was forced to withdraw from Gareth Southgate's squad for the trip to Montenegro.
The Three Lions boss said at the time: "I think he will go back to his club. Hopefully not too serious, bit of a muscular injury but he won't be right for our second game.”
Spurs boss Mauricio Pochettino has now revealed that the injury should not keep Dier out for too long, though he will not be fit enough to feature at Anfield.
No timescale has also been put on the 25-year-old's recovery.
When asked how long Dier would be sidelined, Pochettino said: "One week, 10 days, two weeks. It's not a big issue but he needs to recover from the problem he suffered against the Czech Republic with the national team.
"We'll see how it is going to improve. He was running today but we need to wait for the resolution.
"Every problem has a different resolution with a different player. We need to wait. We are going to assess him day-by-day, but I don't believe it will be longer than two weeks."
Pochettino will also be without another midfielder in Harry Winks, who has a groin injury, while defender Serge Aurier will have a hamstring issue assessed by the club following his return from international duty.
Spurs are third in the Premier League, 15 points behind Jurgen Klopp's side.